Channel-facilitated membrane transport. (i) We applied our earlier developed theory to analyze blockage of Anthrax channel by multi-charged high-affinity toxin inhibitor. (ii) The effect of inter-particle interaction on particle transport through conical channels was studied both analytically and numerically. We showed that flux symmetry inherent in transport of non-interacting particles was broken by inter-particle repulsion. Our analytical predictions were in excellent agreement with numerical results obtained from Brownian dynamics simulations. Dynamics of morphogen gradients in the Drosophila Embrio. We developed a theory of local time that characterized formation of the morphogen gradient in a Drosophila Embrio. Our results show how the local time depends on the distance from the source of the morphogen and the distribution of the morphogen source intensity. Transport in complex media with entropy traps and barriers. Brownian dynamics simulations were used to study the dependence of the effective mobility and diffusion coefficient of a particle on the driving force in tubes of varying shape. Our results show that the dependences may be qualitatively different depending on the shape of the tube, i.e., the tube entropy potential.